Time Domain Reflectometry Measurements of Water Content and ElectricalConductivity of Layered Soil Columns

A. Nadler,* S. Dasberg, and I. Lapid

ABSTRACTThe major argument for measuring the soil salt concentration and

water content at the same position is their high correlation and spa-tial variability. Time domain reflectometry (TDK) was used for si-multaneous measurement of soil water content, 9 (derived from thesoil dielectric constant «), and bulk soil electrical conductivity, a,(from the attenuation of a transmitted pulse), for uniform and layeredsoil profiles in the laboratory. The purpose of the study was to testthe different concepts of travel time and attenuation by using in-dependent estimates of 0 and <r,. Both parallel (two-rod) and simu-lated coaxial (three-rod) probes resulted in essentially the same t.The three-rod probe measurements were easier to interpret and didnot necessitate an impedance-matching transformer. The TDK mea-

A. Nadler and S. Dasberg, Agricultural Research Organization, theVolcani Center, Bet Dagan 50250, Israel; and I. Lapid, Dep. of Iso-tope Research, the Weizmann Institute of Science, Rehovot 76100,Israel. Contribution from the Institute of Soils and Water, Agricul-tural Research Organization, the Volcani Center, no. 2931-E, 1990series. This research was supported by a grant from the USA-IsraelBinational Agricultural Research and Development Fund. Received20 Feb. 1990. "Corresponding author.Published in Soil Sci. Soc. Am. J. 55:938-943 (1991).

surements of 6 for layered profiles were not always accurate, espe-cially when wet soil was overlying dry soil, due to erroneousinterpretation of the TDK trace. In this case, the pulse travel timeshould be measured at the inflection point, which is sometimes dif-ficult to identify, and not at the minimum of the TDK trace. Thisstudy reports a new method of calculating a,, which is based on adirect measurement of the transmission-line load by TDR. This newmethod, which is simpler than the previous ones and independentof multiple reflections, was found to correlate better than the pre-viously published methods with another, independent method for <r,measurement (four-electrode technique).

TIME DOMAIN REFLECTOMETRY has become an es-tablished method to measure both soil volumet-

ric water content (O) and bulk soil electricalconductivity (0-a). It is based on measuring the traveltime (O and the attenuation of the amplitude of anelectromagnetic pulse launched along a transmissionline (TL) of unknown length (L) embedded in the soil.The measurement has been developed by Topp et al.

NADLER ET AL.: TIME DOMAIN REFLECTOMETRY MEASUREMENTS OF SOIL COLUMNS 939

(1980), who showed that for many soil materials thereexists a general empirical 6 = f(e) relationship of theform6 = -0.053 + 0.29e - 5.5 10~4 e2

+ 4.3 10-6 e3 [1]where«, the dielectric constant of the soil, is measuredfrom the t of an electromagnetic pulse through the soilby

€ = (ct/2LY [2]where c = velocity of light in free space. In commercialTDR instruments, the term ct/2 is reduced to an ap-parent TL length (1) resulting in

e = d/L? [3]Coaxial transmission lines were used in the early ap-plications (Topp et al., 1980). Later work showed thatparallel transmission lines (two-rod probes) with animpedance-matching pulse transformer are more con-venient for in situ determinations (Topp et al., 1982).Recently Zegelin et al. (1989) proposed to use simu-lated coaxial transmission lines, i.e. three- or four-rodprobes. This has the advantage that no impedance-matching pulse transformers are needed and the mask-ing of attenuation of the signal by the mismatchedimpedance and by the pulse transformer itself is solvedto a great extent.

Measurements of 0 of layered profiles by TDR wascarried out by Topp et al. (1982). They assumed ad-ditivity of the travel times through overlying layers,resulting in the fact that the TDR-measured 6 of alayered soil was equal to the weighted average of theactual 0 of the layers. A computer algorithm, based ona model for multiple reflections from layered dielec-trics, was developed to calculate the dielectric constantof each layer in the medium (Yanuka et al., 1988). If,however, more than two layers were present, it wasnecessary to extend calculations to include reflectionsof higher than first order and the model had a limitedprecision as a measurement of t.

Subsequently, it was shown that the attenuation ofthe signal can be used as a measure of <ra (Dalton etal., 1984). However, the exact interpretation of theattenuation for this purpose is still somewhat contro-versial, as will be shown.

The purpose of this study was to test the differentconcepts of travel time and attenuation for both lay-ered and uniform profiles by using independent esti-mates of 6 and <ra: volumetric soil sampling,measurement with a four-electrode probe (4P;Rhoades and van Schilfgaarde, 1976) and by compar-ison with a newly suggested method. Moreover, thepossible use of the three-rod coaxial probes (3RTL),compared with the common two-rod parallel probes(2RTL) with a pulse transformer, was evaluated underdifferent <ra and 8 conditions for uniform and layeredprofiles.

THEORYFour significant voltage values are routinely measured on

the TDR trace that appears on the screen V0, Vlt V2, and V{,being amplitudes of TDR pulse, signal after partial reflectionfrom the start of the probe, signal after reflection from theend of the probe, and reflected signal after a very long time

(t » t oo » lOt of Eq. [2]), respectively. Calculation proce-dures suggested for using these voltages in order to obtain<ra are the following.

Dalton et al. (1984) proposed the first approximation forthe calculation of aa (<7D), based on electromagnetic field the-ory:

where Vt is the magnitude of the signal that enters the TLand V-i is the magnitude of the reflected signal (see Fig. 1A).Later work showed that, especially with media of low con-ductance, multiple reflections occur (Topp et al., 1988).

Dalton et al. (1984) used F1e-2aL as an expression for thereflected pulse, while a direct consideration of the reflectedpulse after one round trip was suggested by Topp et al.(1988), who obtained an approximation of <ra (<rT) by usingthe expression Vl + (V2 — K,)̂ "2"1- for the reflected pulsemagnitude, a being the attenuation coefficient resulting, asshown by Zegelin et al. (1989), inOT = (e'/2/1207rL) ln{F,(2F0 -

[F0(F2 - F,)]} [5]Yanuka et al. (1988), using a more rigorous theoretical ap-proach, correcting for multiple reflections as applied by Ze-gelin et al. (1989) obtained an approximation of aa:«TY = (eW/120TrL)ln{[ViVf ~ VQ)Vi + Vf)}/

[Vo(Vi - Vf)}} [6]Recently, Zegelin et al. (1989), following a suggestion fromTopp et al. (1988), adapted the thin-sample analysis of Gieseand Tiemann (1975), which estimates <ra by

= («'/Vl20rL) - Ff)/(2F0 - K,)] [7]

In order to overcome multireflection interferences causedby impedance discontinuities, and also to simplify a& mea-surement by reducing the number of parameters needed forthe calculation, the following new procedure is suggested. Itis based on the fact that, at very long distances along thetrace, all the reflections are suppressed and the signal ap-

3RTL 2RTL

6 9 12 0 3• T I M E HO'9 s i

12

Fig. 1. Time domain reflectometry (TDK) traces obtained with three-rod coaxial probes (3RTL) and with two-rod parallel probes(2RTL) for (A,B) uniform wet saline, (C,D) dry/wet, (E,F) wet/dry, and (G,H) saline wet/dry profiles. Arrows indicate pointswhere the upper and lower layers terminate. V0 = amplitude ofTDR pulse, y, = signal after partial reflection from start of probe,Y! = signal after partial reflection from end of probe, and Vf =reflected signal after a very long time.

940 SOIL SCI. SOC. AM. J., VOL. 55, JULY-AUGUST 1991

proaches a constant value (Kf) representing the impedanceof the direct-current component only. The Vt (which is ac-tually the reflection coefficient) is independent of the TLconfiguration, transfer efficiency of pulse energy, or multiplereflection.

The ratio of the reflected signal amplitude to the incidentsignal amplitude is measured by the 1502 TDR cable tester(Tektronix, Beaverton, OR) as a vertical deflection, whichis called the voltage reflection coefficient (p). It can be usedto determine the impedance of the TL according to

= (RL- Z0)/RL + Z0) [8]where Z0 is the characteristic impedance of the cable (50 Qin our case) and RL is the load of the TL embedded in themedium under investigation. The p values are read directlyfrom the instrument screen. Therefore, measuring the am-plitude of the signal at t —> « gives p values from which theload of the TL (RL of Eq. [8]) can be calculated, and con-verted to <ra by using the probe's geometric constant.

The geometric constant (JQ was experimentally obtainedby immersing the TL in a solution of known salinity (<ra),measuring the resistance RL by TDR, and using an equationidentical to Rhoades and van Schilfgaarde (1976) Eq. [2].

K, = <rref(250) RJft [9]

(ft = temperature-correction coefficient).For example, for a 0.2-m-long TL probe that was intro-

duced into a 1.04 dS nr1 CaCl2 solution, V{ and V0 valuesobtained were 4.2 and 5.1 division units, respectively, at a0.2 m division-' setting. The calculated reflection coefficientis equal to — 0.18 m, and, according to Strickland (1970, Fig.3-5) equivalent to 34.7 fl. Introducing a& = 1.04 dS m-' andRL = 34.7 fi into Eq. [9] results in A; = 36.1.

This calibration was repeated for several TL probes ofsizes 0.1, 0.2, 0.3, and 0.4 m and several solutions (of elec-trical conductivity [EC] 1.04, 2.0, and 4.0 dS m-'). The geo-metric constant Kc was found to be independent ofexperimental conditions and could be determined only once.

MATERIALS AND METHODSGilat soil (silty loam, Calcic Haploxeralf). taken from the

plow layered, dried, and sieved (<2 mm) was used in alldeterminations. A 10-L plastic bucket (0.24-m diam., 0.24-m depth) was packed to uniform density with soil wettedwith either distilled water or NaCl or CaCl2 solutions (EC= 3.9 dS m-1). The soil was thoroughly mixed while sprayingthe solution and brought to equilibrium by storage for sev-eral days. Six increments of wetting in the range of 0.07 to0.28 m3 m-3 were employed with each solution. The soilcontainer was packed either uniformly or in two layers ofseveral wet/dry, saline/nonsaline combinations as specifiedbelow. The depth of the lower layer was 0.14 m, and it wasseparated by a flexible fiberglass screen (177 j&m) from the0.10-m upper layer, which the TL could easily penetrate.

The apparent length, /, of the 0.20-m TL and the magni-tude of the transmitted and reflected signals were measuredwith a 1502 TDR cable tester connected to the TL by a 50-J) coaxial cable (Rb 58A/u). Two types of TL were used ineach measurement: (i) a parallel 2RTL, where the rods weretightly held in a 3-cm-wide, 9-cm-diam. polyvinyl chloridedisk installed with an impedance-matching pulse trans-former (T.P. 103, Adams-Russell Co., Burlington, MA) and(ii) a simulated coaxial 3RTL, cemented to a 13 by 5.5 by1 cm perspex block by chloroform-dissolved perspex, di-rectly connected to the TDR meter, according to Zegelin etal. (1989). Length (0.2 m), distance between rods (0.05 m),and rod diameter (0.003 m) were the same in both TL types.

All determinations were made in duplicate with each TLtype inserted twice into the columns. The following mea-

surements were taken by eye, directly from the TDR screen,for each combination of the packed soils (see Fig. 1):/ - the travel distance of the pulse through the soil (or

apparent TL length, indicated by the double-arrowline);

V0 - the TDR pulse output;Vt - the magnitude of the signal after reflection from the

start of the TL;V2 - the magnitude of the signal after reflection from the

end of the TL;Vf - the magnitude of the final reflected signal at t —»°°.

The above signal magnitudes, at the different stages oftransmission or reflection, are reported as relative voltages.

From these, the following parameters were calculated.The dielectric constant («) according to Eq. [3], aD accord-

ing to Eq. [4], <rr according to Eq. [5], oy according to Eq.[6], <TZ according to Eq. [7], and <rref according to Eq. [8] and[9].

Following the TDR measurements, (ra was measured withthe 4P device of Rhoades and van Schilfgaarde (1976). Fi-nally, volumetric soil samples were taken for 6 and o-w de-terminations. The soil-solution electrical conductivity (Odeterminations were converted into <ra values using era = (ajF) + 5In, where F is the formation factor that relates thesoil's EC to soil texture through pore-size distribution andsoil water content; d is the empirical ratio between equivalentconductance of clay counter ions to the maximum value ofthis equivalent conductance and /„ is the intercept of thelinear part of the <ra — <rw curve at <rw = 0 (Nadler et al.,1984, Eq. [1]). The values of F, da and /„ at the relevantconditions can be obtained from experimental F — 6, d —<rw, and /„ — clay content relations for the different soils (seeNadler et al., 1984; Fig. 2 and 3 for calculating aa from <rw).

RESULTS AND DISCUSSIONWater Content Measurements

The relationship between the e as measured withTDR and the 0 as obtained by actual soil sampling isgiven in Fig. 2. The relationship as given by Topp etal. (1980) for different soil materials is also shown. Itseems that most of the data can be expressed by arelationship similar, yet not identical, to that of Toppet al. (1980).

The regression equations for the relationship be-tween e and 0 obtained from our data (Fig. 2), com-pared with the relationship published by Topp et al.

H55

ouOi

028

024-

O20

016-

012-

0.06-

0.04-

g<M

16 180 2 4 6 ' 8 10 12 14DIELECTRIC CONSTANT (c)

Fig. 2. The relationship between soil water content and the soildielectric constant for Gilat silt loam with uniform profiles wettedwith distilled water (nonsaline) or NaCl or CaCl2 (saline) and forlayered profiles, compared with the relationship obtained by Toppet al. (1980).

20

NADLER ET AL: TIME DOMAIN REFLECTOMETRY MEASUREMENTS OF SOIL COLUMNS 941

(1980), are given in Table 1. Measurements oft by the2RTL with a pulse transformer were very similar tothe measurements obtained with the 3RTL, as can beseen from the similarity of the regression coefficients.It is clear from Fig. 2 that salinity, either caused byNaCl or by CaCl2 did not affect the t-0 relationship,as was also shown previously (Dasberg and Dalton,1985; Dalton et al., 1984).

In the case of a dry soil overlying a wet soil, separatereflections of the upper layers are difficult to discern(Fig. 1C, D). Occasionally, TDK traces of homoge-neously packed soils may show characteristics similarto Fig. 1C. This, however, does not affect the total edetermined (Table 2). In this combination of dry/wet,e values of the layered soil are similar to the onescalculated by averaging the separately measured ho-mogeneous components. Differences are generallyclose to the experimental precision of the e values, asdetermined by the width of the trace on the TDKscreen (±3-15%).

In the case of a wet soil overlying a dry soil, theapparent pulse travel time through the wet layer maybe artificially measured as longer than its water contentindicates (Fig. 1G, H). The true value of the traveltime through the wet layer should be measured at thepoint where the downward slope of the TDK traceflattens (Fig. IE, F, indicated by the first arrow), whilethe total travel time also includes the almost-horizon-tal section ending in the inflection point (indicated bythe second arrow). When determining 6 values of alayered, wet/dry profile, the layering effect may causeany of the following: (i) reduced accuracy of deter-mined 0 (especially when the wet horizon is also salineand the trace becomes flat), (ii) false identification ofthe upper-layer travel time (but not necessarily of thetotal travel time), or (iii) erroneous 6 values when thee difference between the two layers makes it almostimpossible to discern the inflection point on the trace.Table 1. Regression equation coefficients and standard errors for the

relationship between dielectric constant (t) and water content (0)for different transmission line (TL) types, using the equation 0 =(A + Bt + Ci2 + Df3) X 10-*.__________________

Experiment____a A____B_____C_____D R1

Topp et al. (1980) -530 292 -5.5 0.043All data 134 -725 367 ± 56 -12.3 ± 5.4 0.15 ± 0.16 0.9822RTL(2-rodTL) 67 -799 398 ± 82 -15.0 ± 8.0 0.24 ± 0.24 0.9823RTL(3-rodTL) 67 -700 351 ± 76 -11.0 ± 7.0 0.10 ± 0.21 0.983

Table 2. A comparison between dielectric constant («) as measuredwith two-rod transmission line (2RTL) for layered profiles and thet values calculated by averaging the separate uniform soil compo-nents.

DescriptionDry/wet

Wet/dry

Upper0.1-m layer

4.954.954.954.955.525.766.767.918.41

10.8913.8818.1720.02

Lower0.1-m layer

11.9013.1415.8017.6416.8116.815.525.525.525.525.525.528.41

Average8.439.05

10.3711.3011.1611.286.146.726.978.219.70

12.7714.22

Time domainreflectometry

measured8.419.468.70

11.2210.2411.306.257.027.028.70

10.738.12

13.69

Fortunately, the probability of coming across a com-bination of such extreme water contents at close prox-imity under natural conditions is rare and it is,therefore, expected that most TDR-determined 0 val-ues will be free from this error. As can be seen in Table2, most B values of layered (wet/dry) soils are withina few percentage points of the expected values ob-tained by averaging with Eq. [ 12] of Topp et al. (1982).The false result in the single case of 36% deviation wasobtained despite the fact that we expected a layeringeffect, but the visual appearance of a clear-cut minimalpoint in the TDK trace was completely misleading andthe inflection point could not be discerned. It shouldbe taken into account, however, that when TDK in-struments with a digital output are used and the al-gorithm is based on the minimum reading and not onthe inflection point (Dalton, 1989, p. 30 and AppendixC) this may introduce serious errors in the case of wet/dry layering.

Previous work by Topp et al. (1982) has shown thatthe TDK-measured water content in nonuniform pro-files was equivalent to the average sampled water con-tent for both wet/dry and dry/wet profiles. Theirtheoretical analysis assumed a simple addition of trav-el times through the two layers, ignoring the possibilityof interference. Their experimental data seem veryconvincing (Topp et al., 1982, Fig. 6 and 7). However,no independent measurements for 6 for the two layerswere available for most of the data points, which wereobtained by estimating the depth of the initial layerfrom its known 8 and the travel time of the pulsethrough this layer. The depth of the second layer wasobtained by subtraction from the total depth. More-over, our data show that, under certain circumstanceswith the equipment used, it was very difficult to obtainseparate reflections of the upper and lower layer, asshown in Fig. 3 of Topp et al. (1982).Electrical Conductivity of Bulk Soil MeasurementsThe <ra values as a function of probe type, calculation

methods, and matrix homogeneity (relating to watercontent and salinity levels) are presented in Fig. 3 to6.

0.8-

0.6-c/i•o

0.4 -

0.2-

0.4 0.6

(dS/m)

Fig. 3. Relationship between bulk soil electrical conductivity (ojobtained by a four-electrode probe and <rref, the reference methodbased on single reflections, obtained by time domain reflectometryusing the two-rod parallel probe (2RTL) for uniform and layered(high and low water content) profiles (solid line is 1:1 ratio).

942 SOIL SCI. SOC. AM. J., VOL. 55, JULY-AUGUST 1991

c/i•O

0.8

0.6-

0.4-

0.2

2RTL, « • '

A 4

S»^"J**

,»+** + ZEBBM

o YANUKA

A OALTON

X TOPP

0.2 0.4 0.6(dS/m)

0.8

Fig. 4. Relationship between bulk soil electrical conductivity (<rjobtained for uniform profiles by measuring with the two-rod par-allel probe (2RTL) and by using the calculation procedures ofZegelin et al. (1989) (Eq. [7]), Yanuka et al. (1988 (Eq. [6]), Daltonet al. (1984) (Eq. [4]), and Topp et al. (1988) (Eq. [5]) as a functionof <7ref, determined using the reference method based on singlereflections.

0.8

0.6(A•O

a 0.4-

0.2-

~r~5~3RTL

YANUKA

DALTON

0.2 0.43ref

0.6 0.8(dS/m)

Fig. 6. Relationship between bulk soil electrical conductivity (ajvalues obtained for uniform profiles by measuring with the three-rod coaxial probe (3RTL) and by using the calculation proceduresof Zegelin et al. (1989) (Eq. [7]), Yanuka et al. (1988) (Eq. [6]),Dalton et al. (1984) (Eq. [4]), and Topp et al. (1988) (Eq. [5]) asa function of <rref, determined using the reference method basedon single reflections.

0.8-

0.6-

id 0.4-

0.2-

3RTL

0.2 0.4 0.6(dS/m)

0.8

Fig. S. Relationship between bulk soil electrical conductivity (crj,obtained by four-electrode probe, and anf, determined using thereference method based on single reflections, and obtained by timedomain reflectometry using the three-rod coaxial probe (3RTL)for uniform and layered (high and low water content) profiles(solid line is 1:1 ratio).

Two-Rod Parallel ProbesThe ffa values obtained for uniform and layered

matrices by the 4P technique are in excellent agree-ment with values obtained by the reference procedure(Eq. [8] and [9]; Fig. 3). Moreover, a similar agreementexists between <ra obtained by the reference methodwith yet another, independent method (Nadler et al.,1984) shown in Table 3. The <ra for uniform soil pro-files was calculated according to the reference proce-dure (Eq. [8]) from the crw of the soil solution,determined in the 1:1 extract. This procedure was de-veloped for the same (Gilat) soil as used in our study.It is, therefore, not surprising that there was a verygood agreement between the 4P-measured <ra values andthe values calculated from o-w. At low water contents,

it is difficult to obtain good estimates of <ra by the 4Pmethod, since this method is essentially a measurementof total soil resistivity and the contribution of the solid-phase component becomes dominant. Under condi-tions of low salinity, the procedure of Nadler et al.(1984) fails, because <ra values are consistently low andindependent of the av values.

In Fig. 4, ffa values are shown, calculated accordingto the Zegelin et al. (1989) procedure (Eq. [7]), thatare consistently lower relative to the other proceduresand do not seem a valid estimate of <ra. This is contraryto the results of Zegelin et al. (1989), who reported agood agreement of tra values obtained by an alternatingcurrent conductivity bridge and TDK measurements.They calculated o-a from TDR measurements using Eq.[7], which is based on the thin-sample analysis of Gieseand Tiemann (1975), theoretically valid for samplesonly a few millimeters thick. The other three proce-dures (Eq. [4], [5], and [6]) show a better agreementwith the <rref measurement.

From experimental data obtained using the 2RTL(Fig. 3 and 4) it is evident that: (i) the good agreementbetween the 4P and a^ is independent of layering(either 8 or salinity); (ii) the only other calculationprocedure of TDR measurements that agrees withthese two is the calculation of Dalton et al. (1984) (Eq.[4]); (iii) the calculations of Topp et al. (1988) andYanuka et al. (1988) (Eq. [5] arid [6], respectively)deviate slightly towards higher values; and (iv) cal-culations after Zegelin et al. (1989) cause aA to grad-ually depart from the true values with increase ofsalinity. The regression relations between the calcu-lated and reference values are given in Table 4.

Three-Rod Coaxial ProbesThe same relationship between 4P and ffref holds true

also for the 3RTL except for a tendency towards higher(»12%) ffa values in both the uniform and layered

NADLER ET AL.: TIME DOMAIN REFLECTOMETRY MEASUREMENTS OF SOIL COLUMNS 943

Table 3. Electrical Conductivity (EC) of bulk soil (a,) as measuredwith a four-electrode probe, aref by time domain reflectrometryusing two-rod transmission line, and (EC of soil solution?,) foruniform soils.

Table 4. Parameters of the regression equation <ra •• A + Ba^ for

Soil watercenterm'm-3

0.0740.0780.0870.0930.1030.1100.1100.1220.1230.1590.1640.1530.1910.2010.1920.2250.2380.2460.2690.2770.275

<r. of soilsolutions

4.725.904.773.505.824.604.135.135.502.194.424.801.863.954.151.663.293.201.463.403.26

Nadleret al., 1984

JO————— as

______

0.2100.2250.2000.2800.2700.2550.3800.3700.3150.5950.6200.4410.8770.882

a. according to:Four-electrode

probem-' ———————

0.0490.0950.0990.1190.16901740.1290.2240.2050.1950.2980.2860.2510.3880.4090.3140.6160.6090.4320.8790.877

"ref

0.0830.1210.1270.1320.1840.1770.1530.1950.2270.2160.3370.2950.2750.4230.4180.3370.6150.6080.4800.9040.840

matrixes (Fig. 5). The <ra values obtained by the 3RTL,relative to those obtained by the 2RTL, are largerwhen applying the procedure of Dalton et al. (1984)and are characterized mainly by a larger intercept(«0.2 dS nv1; Table 4). The aa values calculated usingTopp et al. (1988) and Yanuka et al. (1988) proceduresare not affected by TL type, although they relate to <rrefby higher intercepts and lower slopes (Table 4).

CONCLUSIONSVolumetric soil water contents were found to be

accurately determined by the TDK method, regardlessof TL type or soil layering, except in the case of verydry overlying very wet soil. This may be attributed tothe difficulty in interpreting the TDK trace and not tothe basic principles of the TDR technique. No signif-icant preference can be related to either of the TL typesand, from Fig. 2 and Tables 1 and 2, it is obvious thatboth probes give similar results. The 3RTL may bepreferred, however, due to the displaying of a simpler(less disturbed by reflections) trace that enables a bet-ter definition of the travel-time boundaries. Pulse trav-el time along the TL should be measured at the lastinflection (and not the minimal) point, especially inthe case of horizons having extreme 8 values overlyingeach other.

Using two independent methods of o-a determina-tion, it was shown that the newly suggested o-ref andthe calculation procedures of Dalton et al. (1984) arethe most suitable for calculating tra from TDR mea-

the relationships between bulk soil electrical conductivity (O cal-culated from the time domain reflectrometry measurements usingdifferent procedures and ow using two-rod transmission line(2RTL) and three-rod transmission line (3RTL) probes (includinga. by the four-electrode probe technique [4P]).

Calculationprocedure4PDalton et al., 1984Topp et al., 1988Yanuka et al., 1988Zegelin et al., 19894PDalton et al., 1984Topp et al., 1988Yanuka et al., 1988Zegelin et al., 1989

Probetype_

2RTL2RTL2RTL2RTL_3RTL3RTL3RTL3RTL

n71717171717171717171

A-0.002

0.0970.1260.0430.053

-0.0030.2440.1350.0450.040

B1.0010.9471.2361.3570.4811.1200.9631.2661.2780.500

i*0.9800.9420.9720.9810.9620.9770.9630.9570.9710.957

surements, including the case of layering. The pros-pects of the TDR method to replace the 4P methodare good because the attenuation of an electromagneticpulse, which is the basis for TDR determination of o-a,is insensitive to quality of contact between the probeand the medium and, therefore, may be a more validestimate of real bulk soil electrical conductivity.